Does it really matter?
You dont have to emulate EVERYTHING a Gadol does.
I heard a story how a gadol wouldnt eat chicken and then all his talmidim wouldnt eat chicken either because he wouldnt eat it, One day someone asked him what is the reason he doesnt eat chicken and his answer was I dont like the taste of it.
But to answer your question, It is not a Tzniut or any other halachic reason, He has an issue with his eyes and he cant really be exposed to sunlite.